Branch & Bound 34 8 7 12 10 9 3 6 8 2 7 0 0 UPPER =  LOWER = 0.

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Presentation transcript:

Branch & Bound UPPER =  LOWER = 0

Branch & Bound UPPER =  LOWER = 2

Branch & Bound UPPER =  LOWER = 3

Branch & Bound UPPER = 4 LOWER = 4

UPPER = 3 LOWER = 3 Branch & Bound

UPPER = 3 LOWER = 6 Branch & Bound

UPPER = 3 LOWER = Branch & Bound

Tasks are created dynamically Upper bound is shared Lower bound is local Halve set of feasible tours: Explore only those paths that visit city 1 before city 2. Branch & Bound Illustrated on Traveling Salesman Problem

:0 01:1 02:4 03: :2013: : : :5032:2 41 Partial tour 0, 3, 2 with cost lower bound = 2 LEGEND TSP instance Search Tree Halve the set of feasible tours: Only visit tours where city 1 occurs before city 2.

:0 01:1 02:4 03: :2013: : : :5032:2 41 Partial tour 0, 3, 2 with cost lower bound = 2 LEGEND upper bound =  TSP instance Search Tree